A Quantum Leap For Cryptography

May 5, 20100

An international team of researchers has found a way to make random numbers truly random. The study, published in the journal Nature, was supported by the EU through the PERCENT (‘Percolating entanglement and quantum information resources through quantum networks’) and QORE (‘Quantum correlations’) projects, which received $8.97 million (EUR 7) million and $2.5 million (EUR 2 million) respectively from the European Research Council (ERC). Funding also came from the QAP (‘Qubit applications’) project, funded with $12.7 million (EUR 9.9 million) under the ‘Information society technologies’ Thematic area of the Sixth Framework Programme (FP6).

To create random number lists for encryption purposes, cryptographers usually use mathematical algorithms called ‘pseudo random number generators’. But these are never entirely ‘random’ as the creators cannot be certain that any sequence of numbers isn’t predictable in some way.

Now a team of experimental physicists has made a breakthrough in random number generation by applying the principles of quantum mechanics to produce a string of numbers that is truly random.

‘Classical physics simply does not permit genuine randomness in the strict sense,’ explained research team leader Chris Monroe from the Joint Quantum Institute (JQI) at the University of Maryland in the US. ‘That is, the outcome of any classical physical process can ultimately be determined with enough information about initial conditions. Only quantum processes can be truly random – and even then, we must trust the device is indeed quantum and has no remnant of classical physics in it.’

According to the laws of quantum mechanics, the properties of objects are by their very nature uncertain. Although the probability of any particular property can be calculated in advance, those properties take on particular value only when measured. Therefore, theoretically, it is possible to obtain a set of random numbers by carrying out a series of quantum measurements that are completely independent of each other.

The researchers used a revolutionary technique known as ‘private randomness’, which was invented by the Irish physicist Dr John Bell in 1964 in order to test the quantum mechanics hypothesis that two objects such as photons or matter particles can enter a condition called ‘entanglement’. This means they become interdependent, so if a measurement is carried out on one, the corresponding property of the other is determined, even if they are separated by large distances.

‘Bell inequalities entail measurements on an entangled pair that allow us to quantify this entanglement,’ Professor Monroe told Research Headlines. ‘Now to do the cleanest Bell inequality test, you should be able to satisfy two conditions. First, the particles should be separated by a distance far enough that it is impossible for them to communicate (otherwise you could claim that they “could have” communicated to get correlated). Second, you must be able to record each and every event. If you flip a single fair coin 1 000 times but only record 50 of the outcomes, and they are mostly heads, it’s still possible that the coin is fair.’

The technique involves counting correlations between measurements made on the two objects as the measuring devices are switched between different orientations. Dr Bell proved mathematically that if the objects were not entangled, their correlations had to be smaller than a certain value, expressed as an inequality. If they were entangled, the correlation rate could be higher, something that would violate the inequality.

In this experiment, the team placed single atoms in two spaces a metre apart and entangled them. Each time that their apparatus signalled that entanglement had been achieved, the team rotated each atom on its axes according to a random schedule and took a measurement of the light emitted by each atom. The value from each of two atoms was then used to generate a binary number.

Altogether more than 3 000 entanglements were achieved, generating 42 random private binary digits at 99% confidence levels. The researchers write, ‘We can for the first time certify that new randomness is produced in an experiment without a detailed model of the device.’

The experiment was the first to violate the inequality between objects separated over a distance without missing any of the events. ‘In the cryptography and random number business, you can be fooled by missing a good fraction of the events, and in our experiment we do not miss a single event,’ said Professor Monroe.

‘Violation of a Bell inequality is possible only if the system obeys the laws of quantum mechanics,’ added the JQI’s Dzmitry Matsukevich. ‘Therefore if we verify a Bell inequality violation between isolated systems while not missing events, we can ensure that our device produces private randomness. We don’t need the atoms to be too far apart, only far enough so that they could be shielded from each other, as would be done anyway in a real cryptographic setting.’

‘The random bit generation rate is extremely slow at present,’ commented Professor Monroe, ‘but we expect speed-ups by orders of magnitude in the coming years as we more efficiently entangle the atoms, perhaps by using atom-like quantum systems embedded in a solid-state chip.’ By violating the Bell inequality over much larger distances, he added, ‘such a system could be deployed for a more secure type of data encryption’.